VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY
HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY
Nguyen Thi Xuan Huynh
HYDROGEN STORAGE IN METAL-ORGANIC FRAMEWORK
MIL-88S: A COMPUTATIONAL STUDY
Major: ENGINEERING PHYSICS
Major code: 62520401
PhD Dissertation - Summary
Ho Chi Minh City – 2019
The dissertation was completed in Ho Chi Minh City University of
Technology, Vietnam National University – Ho Chi Minh city.
Scientific Supervisor 1: Dr. Do Ngoc Son
Scientific Supervisor 2: Dr. Pham Ho My Phuong
Independent Reviewer 1: Assoc. Prof. Dr. Pham Tran Nguyen Nguyen
Independent Reviewer 2: Assoc. Prof. Dr. Nguyen Thanh Tien
Reviewer 1: Assoc. Prof. Dr. Phan Bach Thang
Reviewer 2: Assoc. Prof. Dr. Huynh Quang Linh
Reviewer 3: Dr. Phan Hong Khiem
The dissertation will be defended in front of the board of examiners at ............
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on ........................................................................................................................
This dissertation can be found at following libraries:
- The Library of the Ho Chi Minh City University of Technology, VNU-HCM
- Central Library – VNU HCM
- General Science Library – Ho Chi Minh City
LIST OF PUBLICATIONS
I.
Journal articles
[1] N. T. X. Huynh, C. Viorel, and D.N. Son, “Hydrogen storage in MIL-88
series,” Journal of Materials Science, vol. 54, pp. 3994-4010, 2019 (Q1,
IF = 3.442).
[2] N. T. X. Huynh, O M. Na, C. Viorel, and D.N. Son, “A computational
approach towards understanding hydrogen gas adsorption in Co-MIL88A,” RSC Advances, vol. 17, pp. 39583-39593, 2017 (Q1, IF = 3.049)c.
[3] T. T. T. Huong, P. N. Thanh, N. T. X. Huynh, and D. N. Son, “MetalOrganic Frameworks: State-of-the-art Material for Gas Capture and
Storage,” VNU Journal of Science: Mathematics – Physics, vol. 32, pp.
67-84, 2016.
II. Conference reports
[1] D. N. Son, N. T. X. Huynh, P. X. Huong, P. N. Thanh, P. N. K. Cat, and
M. Phuong Pham-Ho, CO2 capture in metal organic framework MIL-88s
by computational methods, International Symposium on Applied Science
(ISAS), Ho Chi Minh City University of Technology (HCMUT), 2019
(accepted).
[2] N. T. X. Huynh, P. X. Huong, and D. N. Son, Hydrogen storage and
carbon dioxide capture in metal organic framework M-MIL-88A (M = Sc,
Ti, V, Fe), First Rencontres du Vietnam on Soft Matter Science, ICISE,
Quy Nhon city, Vietnam, 2019.
[3] N. T. X. Huynh, O. K. Le, and D. N. Son, “Hydrogen storage in metal
organic framework MIL-88D,” The 43rd National Conference on
Theoretical Physics (NCTP-43), Quy Nhon city, Vietnam, 2018.
[4] N. T. X. Huynh, O M. Na, and D. N. Son, “Computational study of
hydrogen adsorption in MIL-88 series,” The 42nd National Conference on
Theoretical Physics (NCTP-42), Can Tho city, Vietnam, 2017.
[5] D. N. Son, N. T. X. Huynh, and O M. Na, “Exploring Hydrogen Gas
Adsorption in Co-MIL-88A by Computational Methods,” The 42nd
National Conference on Theoretical Physics (NCTP-42), Can Tho city,
Vietnam, 2017.
[6] N. T. Y. Ngoc, N. T. X. Huynh, and D. N. Son, “Investigation of hydrogen
adsorption in M(bdc)(ted)0.5 by computer simulation methods,” The 42nd
National Conference on Theoretical Physics (NCTP-42), Can Tho city,
Vietnam, 2017.
[7] P. X. Huong, N. T. X. Huynh, and D. N. Son, “Adsorption of CO2 in
metal-organic framework of MIL-88A by computational methods,” The
i
42nd National Conference on Theoretical Physics (NCTP-42), Can Tho
city, Vietnam, 2017.
[8] N. T. X. Huynh, O M. Na, and D. N. Son, “Influence of trivalent transition
metals in MIL-88A on hydrogen sorption,” Scientific and technological
conference for young researchers - Ho Chi Minh City University of
Technology, HCM city, Viet Nam, 2017.
[9] N. T. X. Huynh, O M. Na, and D. N. Son, “Effects of metal substitution in
MIL-88A on hydrogen adsorption: Computational study,” The Third
International Conference on Computational Science and Engineering
(ICCSE-3), Ho Chi Minh city, Vietnam, 2016.
[10] T. T. T. Huong, P. N. Thanh, N. T. X. Huynh, D. N. Son, “Metal – organic
frameworks: Potential applications and prospective future research,” The
14th Conference on Science and Technology: International Symposium on
Engineering Physics and Mechanics, Ho Chi Minh City University of
Technology, HCM city, Vietnam, 2015.
III. Research projects
[1] Hydrogen and carbon dioxide sorption in metal-organic frameworks of
MIL-88 series: Computational study, Code number: 103. 01-2017.04,
Nafosted Funding, 2017 – 2019 (Research role: PhD student).
[2] Theoretical study of the propagation and the Anderson localization of
waves in complex media, Code number: 103. 01-2014.10, Nafosted
Funding, 03/2015 – 03/2017 (Research role: Technician).
[3] Hydrogen gas adsorption in MIL-88A(Co): A density functional theory
study, Code number: TNCS-2015-KHUD-33, 2015-2017 (Co-principal
investigator).
[4] Study the adsorption capacity of hydrogen gas in Metal-organic
frameworks by simulation method, Code number: T2015.460.05, Quy
Nhon University, 2015-2016 (Principal investigator).
IV. Others
[1] N. T. X. Huynh, C. Viorel, and D.N. Son, “Effect of metal substitution in
MIL-88A on hydrogen adsorption: Multi-scale theoretical investigation”
in preparation.
[2] N. T. X. Huynh, C. Viorel, and D.N. Son, “Hydrogen storage and carbon
dioxide capture in M-MIL-88D metal-organic framework family” in
preparation.
ii
ABSTRACT
Fossil fuel-based energy consumption causes serious environmental impacts
such as air pollution, greenhouse effect, and so on. Therefore, searching clean
and renewable energy sources is urgent to meet the demand for sustainable
development of the global society and economy. Hydrogen gas (H2) is a
reproducible, clean, and pollution-free energy carrier for both transportation
and stationary applications. Hydrogen gas has a much higher energy density
than other fuels; and thus, it becomes one of the most promising candidates to
replace petroleum. Therefore, in recent years, the interest in the research and
development of hydrogen energy has grown constantly. A safe, efficient, and
commercial solution for hydrogen storage is based on adsorption in porous
materials, which have the exceptionally large surface area and ultrahigh
porosity such as metal-organic framework (MOF) materials. In order to be
selected as porous materials for gas storage, MOFs must be stable to avoid
collapsed under humid conditions. MIL-88 series (abbreviated as MIL-88s
including MIL-88A, MIL-88B, MIL-88C and MIL-88D) is highly stable and
flexible sorbents. For these reasons, MIL-88s becomes a suitable candidate for
the storage of hydrogen gas based on the physisorption. Moreover,
coordinatively unsaturated metal centers in MIL-88s are able to enhance gas
uptakes significantly at ambient temperatures and low pressures. These
materials have been investigated and highly evaluated for various applications
such as gas storage/capture and separation of binary gas mixtures in recent
years; however, they have not yet been evaluated for hydrogen storage. These
outstanding features have attracted my attention to consider the hydrogen
storage capacity in MIL-88 series.
In this dissertation, the van der Waals dispersion-corrected density
functional theory (vdW-DF) calculations were used to examine the stable
adsorption sites of the hydrogen molecule in MIL-88s and clarify the
interaction between H2 and MIL-88s via electronic structure properties. This
observation showed an implicit role of electronic structures on the H2
adsorption capacity at the considered temperature and pressure conditions.
Besides, it was found that the H2@MIL-88s interaction is dominated by the
bonding state () of the hydrogen molecule and the p orbitals of the O and C
atoms in MIL-88s. For MIL-88A and B, the d orbitals of the metals also play
an important role in the interaction with H2.
Moreover, grand canonical Monte Carlo (GCMC) simulations were used to
compute hydrogen uptakes in MIL-88s at the temperatures of 77 K and 298 K
and the pressures up to 100 bar. For Fe based-MIL-88 series, we found that
MIL-88D is very promising for the gravimetric hydrogen storage
(absolute/excess uptakes = 5.15/4.03 wt% at 77 K and 0.69/0.23 wt% at 298
K), but MIL-88A is the best alternative for the absolute/excess volumetric
iii
hydrogen storage with 50.69/44.32 g/L at 77 K and 6.97/2.49 g/L at 298 K. Via
this research, scandium (Sc) was also found as the best transition metal element
for the replacement of Fe in MIL-88A for the hydrogen storage, in which
absolute/excess uptakes are 5.30/4.63 wt% at 77 K and 0.72/0.29 wt% at 298 K
for gravimetric uptakes; 51.99/45.51 g/L at 77 K and 7.08/2.83 g/L at 298 K for
volumetric uptakes. The hydrogen storage capacity is the decrease in the order:
Sc-, Ti-, V-, Cr-, Mn-, Fe-, and Co-MIL-88A. The calculations showed that the
results are comparable to the best MOFs for the hydrogen storage up to date.
The results also elucidated that the gravimetric hydrogen uptakes depend on the
special surface area and pore volume of the MIL-88s. These important
structural features, if properly improved, lead to an increase in the capability of
hydrogen storage in MIL-88s.
iv
INTRODUCTION
1. Motivation for study
Hydrogen gas (H2) is an attractive source for potential clean energy because
it is most abundant in the universe as part of water, hydrocarbons, and biomass,
etc. Moreover, using energy from the H2 gas does not emit the CO2 gas and not
pollute the environment like the burning of fossil fuels. In recent years, the
material-based hydrogen storage is expected to provide the safe, efficient and
commercial solution for hydrogen storage in both transportation and stationary
applications. However, in order to use the hydrogen energy source, most
commonly used in the fuel cell technology, it is necessary to develop a
comprehensive system of generating production, storage, delivery, and fuel cell
technologies for hydrogen. In which, the H2 gas storage has been challenging
because of its low density. Therefore, seeking advanced storage materials plays
a vital role in the success of hydrogen energy technology. The 2020 targets for
the H2 storage set by the U.S. Department of Energy (DOE) are 1.8 kWh/kg (55
mg H2 per gram of the (MOF+H2) system, i.e. 5.5 wt% H2) for gravimetric
storage capacity and 1.3 kWh/L (40 g H2/L) for volumetric storage under
moderate temperatures and pressures (Hwang & Varma 2014). Various
materials have been studied for hydrogen storage such as metal hydrides,
carbon-based materials, zeolites, zeolitic imidazolate frameworks (ZIFs),
covalent organic frameworks (COFs), and MOFs. Among them, MOFs having
the ultrahigh surface area, high porosity and controllable structural
characteristics are the most promising candidates for the commercial hydrogen
storage. Although thousands of MOFs have been successfully synthesized, only
a few of them have been tested for hydrogen storage. MIL-88 series (hereafter
denoted as MIL-88s, where s = A, B, C and D; MIL = Materials from Institut
Lavoisier) has attracted my attention due to consisting of the coordinatively
unsaturated metal sites (CUS), one of the most effective strategic solutions for
improving the gas storage capacity. Furthermore, MIL-88s structures have high
flexibility and thermal stability; and hence, they are expected to be good
candidates for long-term hydrogen storage. Although MIL-88s has been
assessed for catalyst (Wang et al. 2016), NO adsorption (McKinlay et al. 2013),
and CO2 capture (Wongsakulphasatch et al. 2016), they has not yet been
explored for hydrogen storage.
In this dissertation, vdW-DFT calculations are utilized to examine
favourable adsorption sites of H2 in the MIL-88s via the adsorption energy. The
interaction of the H2 molecule with MIL-88 series is also clarified through
electronic structure properties such as the electronic density of states (DOS),
charge density difference (CDD), Bader charge, overlapping DOS between the
gas molecule and MOF, and the overlapping of the wave functions. Besides,
1
grand canonical Monte Carlo (GCMC) simulations are used to assess
quantitatively the H2 storage capability via the H2 adsorption isotherms of MIL88s and the strength of the H2@MOF interaction through the isosteric heat of
adsorption.
2. Structure of PhD dissertation
The structure of this dissertation consists of 6 chapters and the supporting
contents, described as follows
- Introduction: introduce the motivation and the outline of this dissertation.
- Chapter 1: Literature review of metal-organic frameworks: an
overview of MOFs, main applications of MOFs, the overview of experimental
and computational research methods in the literature are introduced.
- Chapter 2: Computational methods: introducing the theory of the
computational methods that are density functional theory (DFT) using revPBE
functional and Grand canonical Monte Carlo (GCMC) simulations. We also
provide computational details for the concerns of this dissertation.
- Chapter 3: Hydrogen gas adsorption in Co-MIL-88A: the hydrogen
adsorption of Co-MIL-88A is studied and the physical origin for the interaction
between H2 and Co-MIL-88A is explained. Firstly, searching for the most
favourable adsorption sites of H2 is performed via computing the adsorption
energy, and then the electronic properties are analyzed based on vdW-DFT
calculations. Finally, hydrogen adsorption isotherms of the Co-MIL-88A are
computed by GCMC simulations.
- Chapter 4: Hydrogen storage in MIL-88 series: MIL-88 series
including MIL-88A, B, C, and D is considered for hydrogen storage capacity.
GCMC simulations quantitatively assess the H2 uptakes of the MIL-88s
sorbents via the H2 adsorption isotherms at 77 K and 298 K with the pressures
below 100 bar using the GCMC simulations. The vdW-DF calculations
elucidate the interaction between the H2 molecule and the MIL-88s.
- Chapter 5: Effects of metal substitution in MIL-88A on hydrogen
adsorption: performing to evaluate hydrogen storage capacity of MIL-88A and
the effects of transition metal substitution on H2 adsorption in M-MIL-88A (M
is Sc, Ti, V, Cr, Mn, Fe, and Co). Moreover, the adsorption energies of H2 with
M-MIL-88A at the side-on and end-on adsorption configurations closing to the
metal centers are calculated by the vdW-DF approach to search the most stable
configurations. Besides, electronic properties are also clarified for the stable
adsorption configurations. Via the GCMC simulations, the hydrogen adsorption
isotherms at 77 K and 298 K and the isosteric heats of hydrogen adsorption in
M-MIL-88A series are also studied.
- Chapter 6: Conclusions and outlook: highlighting the main findings,
scientific contributions, and give an outlook for this topic in the near future.
2
CHAPTER 1: LITERATURE REVIEW OF METAL-ORGANIC
FRAMEWORKS
1.1. General overview of metal-organic frameworks
1.1.1. Definition of metal-organic frameworks
MOFs are the compounds constructed by two main components that are
inorganic metal ions/clusters and organic ligands/linkers (Zhou et al. 2012).
Figure 1.1 shows a simple topology of MOF consisting of metal nodes
connected to organic linkers to form a three-dimensional (3D) framework.
+
Organic Metal ion/
linker
cluster
Figure 1.1. Simple topology of MOFs.
1.1.2. Structural aspects of MOFs
1.1.2.1. Primary building units
The metal ions connecting with the organic ligands are basic primary units
resulting in the porous 3D structure of MOFs. Therefore, metal ions and
organic compounds are used as the primary building units (PBUs) of MOFs.
1.1.2.2. Secondary building units
Organic ligands of MOFs are connected via metal-oxygen-carbon clusters,
instead of metal ions alone. These metal-oxygen-carbon clusters are called as
secondary building units (SBUs). SBUs have intrinsic geometric properties,
facilitating MOF’s topology.
1.1.3. History of MOFs
During the last two decades, MOFs continuously set new records in terms of
specific surface area (SSA), pore volume, and gas storage capacities. MOF-177
and MOF-210 are the two of MOFs which have been technically tested for H2
storage and CO2 capture with exceptionally high storage capacity at 77 K and
relatively low pressure ( 100 bar). Reported to date, NU-109 and NU-110
exhibited the highest experimental BET surface area (SBET) with 7000 m2/g and
7140 m2/g, respectively (Farha et al. 2012). Nowadays, thousands of different
types of MOFs have been known and they have been continuously developing
further. In general, SSA of MOFs is much larger than the surface area of other
traditional inorganic materials such as zeolites, silicas (< 1000 m2/g), and
activated carbons (< 2000 m2/g). Pore volume is also one of the most important
characteristics affecting the adsorption capacity of porous materials.
3
1.1.4. Nomenclature
MOFs have been named either by a sequence of isoreticular synthesis, the
sequential number of synthesis/chronological order of discovery or the initials
of the Institution or Laboratory where they were first synthesized.
1.1.5. Current research of MOFs in Vietnam
In Vietnam, MOFs have been studied by several research groups, e.g., the
experimental research group of Nam T. S. Phan (Faculty of Chemical
Engineering, HCMC University of Technology), the Center for Innovative
Materials and Architectures (INOMAR), VNU-HCM; Institute of Materials
Science and Institute of Chemistry, Vietnam Academy of Science and
Technology (VAST), Ha Noi; Institute of Chemical Technology, Vietnam
Academy of Science and Technology; University of Sciences, Hue University,
University of Science, VNU-HCM and so on. In addition to our computational
research group, the groups of Dr. Nguyen-Nguyen Pham-Tran (Faculty of
Chemistry, University of Science, VNU-HCM) and Dr. Hung M. Le
(INOMAR) also have studied the MOFs by DFT and GCMC simulations.
1.2. Major applications of MOFs
Due to the flexible combination of organic and inorganic components,
MOFs offer many outstanding structural characteristics such as exceptionally
large surface areas, high pore volume, ultrahigh porosity, complete exposure of
metal sites, and high mobility of guest species in the nanopores of frameworks.
MOFs can be widely used for many applications such as catalysis, gas capture
and storage, gas separation/purification, sensing, biological application, and
semiconductors, etc.
In 2003, hydrogen storage was firstly investigated on MOF-5 with the
uptakes of 4.5 wt% (78 K, 0.8 bar) and 1.0 wt% (298 K, 20 bar) (Rosi et al.
2003). This report has attracted much attention and opened a new research
direction for computational simulations. Assessment of hydrogen storage in the
MOF was firstly calculated in 2004 using GCMC simulations and UFF by
Ganz group (Sagara et al. 2004). Up to now, the experimental record in the
highest total (or absolute) H2 uptake was found in MOF-210 with 17.6 wt% at
77 K and 80 bar (excess uptake = 8.6 wt%) (Furukawa et al. 2010). The highest
excess H2 uptake is of NU-100 with 9.95 wt% at 56 bar and 77 K (absolute
uptake = 16.4 wt% at 70 bar) (Farha et al. 2010). Due to the weak H2@MOF
interaction and the low isosteric heat of H2 adsorption (typically 4 – 13 kJ/mol),
hydrogen uptakes of MOFs exhibited significant only at cryogenic temperature
and quite low at room temperatures, the highest ca. 1.0 wt% for excess uptake
and 2.3 wt% for absolute uptake. Although none of MOFs has reached the
DOE targets at room temperatures, they contain several key characteristics that
are expected to improve and ultimately produce new MOFs with exceptional
4
properties for hydrogen storage. Various solutions for improving the storage
capacity at ambient temperature have been suggested. One of the most effective
solutions is using the MOF containing CUS. In recent years, the supports from
computer simulations allow predicting and designing new MOFs that can
significantly improve hydrogen uptakes.
1.3. Overview of synthesis and research methods for MOFs
1.3.1. Synthesis methods for MOFs
MOFs are synthesized by the combination of organic ligands and metal salts
in solvothermal reactions at relatively low temperatures (below 300C). The
reactants are mixed in the boiling and polar solvents which are water, dialkyl
formamide, dimethyl sulfoxide, acetonitrile and so forth.
1.3.2. Theoretical studies
Nowadays, theoretical studies have been proven to be useful to help
explaining what is happening in the experiments and reduce expensive, difficult
and time consuming experimental studies. The application of computational
methods to investigate H2 adsorption properties of MOFs has been identified as
crucial to the direction of finding an efficient solution to the hydrogen storage
problem, see Ref. (Tylianakis et al. 2011) and references therein.
1.4. MIL-88s for hydrogen storage
Although thousands of MOF structures have been synthesized, only a few of
them were evaluated for hydrogen storage, especially at ambient temperatures
and low pressures. Among them, I pay attention to the MIL-88 series which has
been studied for many potential applications. MIL-88 series is interested in
hydrogen storage because of the following reasons:
MIL-88 series has very high flexibility and stability, which can avoid
being collapsed if it is exposed to a humid environment.
MIL-88s containing exposed metal sites is one of the most effective
solutions to improve gas adsorption.
So far, MIL-88 series has not yet been evaluated for H2 storage.
In this dissertation, MIL-88 series is investigated for the first time for H2
storage by using the most up-to-date and reliable version of computational
methods which are the dispersion-corrected version of density functional theory
calculations in combination with grand canonical Monte Carlo simulations.
Through analysis of the results, the capability of utilizing MIL-88 series for
hydrogen storage can be gauged. Moreover, the scientific results are new and
become important references for experimental researches, contributing to the
field of hydrogen storage for the energy application.
5
CHAPTER 2: COMPUTATIONAL METHODS
2.1. Density functional theory calculations
2.1.1. The Schrödinger equation
Many-body problem is a vast physical one relating to the properties of
microscopic systems made of a large number of interacting particles, covered
by the time-dependent Schrödinger equation in a general form as follows:
(2.1)
Hˆ (r , R, t ) E(r , R, t ),
where E is the total energy and is the wave function, Ĥ is the Hamiltonian
operator is given by
(2.2)
Hˆ Tˆe TˆN Vˆee (r ) VˆNN ( R) VˆNe (r , R),
in which r stands for a set of r1 , r2 ,
electrons, and R = R1 , R2 ,
, RN
, rNe
that are the coordinates of Ne
that are the coordinates of N nuclei.
Substituting for Ĥ in (2.1) by using (2.2), we obtain the following equation
Tˆe TˆN Vˆee r VˆNN R VˆNe r , R r , R, t E r , R, t . (2.3)
Basically, equation (2.3) must be solved to appropriate boundary conditions,
decay to zero at infinity for an atom or molecule or obeying appropriate
periodic boundary conditions for a regular infinite solid. Solving (2.3) will
obtain the energy value E, the wave function , and then the probability
2
distribution function . However, this equation is very difficult to solve
when N is enough large. The system even containing more than one nucleus
with one electron also demands highly time for calculation. Therefore, it is
necessary to use Born-Oppenheimer and adiabatic approximations to separate
this equation into Schrödinger equations for electrons and nuclei.
2.1.2. Born-Oppenheimer and adiabatic approximations
Because the mass of the nuclei is much larger than the mass of the electrons,
the nuclei move much slower than the electrons. Therefore, nuclei can be
considered stationary in the electronic structure calculation. It means that the
movement of nuclei is assumed not to induce excitations in the electronic
system. The nuclei are treated as fixed points in space. Applying these
approximations, we can separate the wave function of the system as follows
(2.4)
where r , R and R, t are wave functions of electrons and nuclei.
r , R, t r , R R , t ,
6
Based on these approximations, the Schrödinger equation can be separated
into two Schrödinger equations of electrons and nuclei
(2.5)
Hˆ e r , R E R r , R
R Hˆ R R, t E R, t .
TˆN VˆNN
(2.6)
e
N
Here Hˆ e Tˆe Vˆee VˆNe is the Hamiltonian of electrons in the system
corresponding to external potential VˆNe describing nucleus-electron
and
interactions; ( R) is the energy of electrons, which depends parametrically on
the ionic positions. The electronic energy is calculated by solving the timeindependent Schrödinger equation (2.5) for the fixed nuclear configuration.
One of the most popular and effective methods is density functional theory
(DFT).
2.1.3. Thomas-Fermi theory
The Thomas-Fermi model is the first density functional theory based on the
uniform electron gas, proposed by Thomas (1927) and independently Fermi
(1928) (Kohanoff 2006).
2.1.4. Hohenberg-Kohn theorems
In 1964, based on the new DFT, Hohenberg and Kohn (Hohenberg et al.
1990) showed that this principle could be generalized to any electronic system.
2.1.5. Variational principle for the ground state
The variational principle states that the energy computed from a guessed Ψ
is an upper bound to the true ground-state energy Eo: E[ ] Eo .
2.1.6. The Kohn-Sham equations
The Thomas-Fermi model provided the first DFT based on the uniform
electron gas; however, its performance is not so good due to the poor
approximation of the kinetic energy; thus, Kohn and Sham proposed a new
approach in 1965 based on the ideas of Hohenberg and Kohn, described below
Supposing the non-interacting Ne-electron system is given by
Ne
2
Hˆ R
i2 uR ri ,
(2.7)
i 1 2me
where uR ri is the reference potential. The Schrödinger equation for one
electron in the system of non-interacting electrons has the form:
Hˆ KS i r ii r , Hˆ KS
7
2
2me
i2 uR ri .
(2.8)
The electron charge density is also determined by r
Ne
r
i
2
.
i 1
The reference potential is determined by
r
u R r VNe r
dr XC r .
r r
Where XC
(2.9)
E XC
, in which EXC EC EX is the
r
correlation and exchange energy. If uR r in (2.9) is determined (i.e. VNe r
and XC r are determined), the Kohn - Sham equation will be solved.
2
2 VNe r
2
m
e
r
r r dr
XC
r i r ii r (2.10)
2.1.7. Self-consistent field methods
By solving the Kohn-Sham equation for a self-consistent loop (Figure 2.1),
we will obtain the output density out r : out r
N
r
i
2
in
i 1
Put a trial density
Calculate the Kohn-Sham potential
Solve the Kohn-Sham equation
Total energy,
force,…
Calculate the new density
Self-consistent?
Yes
No
Figure 2.1. Flow chart of a self-consistent loop of the Kohn-Sham equation.
8
Note that out r and in r (or KS in and KS out ) must satisfy the
self-consistent condition, i.e. they must be equal within a certain error limit in
the energy.
2.1.8. Van der Waals density functional (vdW-DF) calculations
A proper theory for solids and molecules should take into account all types
of interactions consisting of the electrostatic interactions, covalent bonds,
hydrogen bonds, and van der Waals interactions (Klime et al. 2011). However,
the conventional DFT with LDA or GGA cannot capture the van der Waals
interactions. London dispersion interactions contribute to the stability of a wide
variety of systems ranging from biomolecules to molecules adsorbed on the
surface of materials. Among them, the van der Waals dispersion-corrected
density functional theory (vdW-DF) method has been received great attention
since it can be incorporated with the DFT framework.
2.1.9. Computational details
For the study of favourable adsorption sites and electronic structure
properties, the Vienna ab initio simulation package (VASP) (Kresse &
Furthmüller 1996) with vdW-DF calculations of Lundqvist et al. (Dion et al.
2004) was employed. The plane-wave basis set with the cut-off energy of 700
eV, the revBPE functional for the exchange-correlation energy, and the
projector-augmented-wave method for the electron-ion interaction were used to
perform the calculations. The surface Brillouin-zone integrations were
performed by using the Monkhorst and Pack k-point sampling technique with
the 444 grid and the Gamma point at the centre. The Methfessel-Paxton
smearing of order 1 was used for the geometry relaxation with the smearing
width sigma of 0.1 eV. However, the linear tetrahedron method with Blöchl
corrections was employed for the calculations of total energy. For computing
the favourable adsorption sites of hydrogen molecule (H2) in the MIL-88s, we
calculated the adsorption energy (Eads) of H2 in the MOF by using the equation:
where E[MOF+H2 ]
Eads Eb E MOF+H2 EMOF EH2 ,
(2.11)
is the total energy of a [MOF + H2] system (i.e. the total
energy of MIL-88A with an absorbed hydrogen molecule); EMOF and EH2 are
the total energy of the pristine MOF, and the isolated hydrogen molecule,
respectively.
2.2. Grand canonical Monte Carlo (GCMC) simulations
2.2.1. Introduction
GCMC simulations have been used to calculate the hydrogen uptake of
MOFs. In this method, the number of particles in the system allowed to change
9
during the simulation process by random test steps such as creation, deletion,
displacement or rotation so that the system reaches to the equilibrium state. The
accuracy of a GCMC simulation describing the interatomic interactions
between the H2 molecule and the MOFs depends on the accuracy of the force
fields, compared with the experimental data. Force fields have been employed
in H2 adsorption simulations that are generic force fields: UFF (Rappe et al.
1992), DREIDING (Mayo et al. 1990) and OPLS (optimized potential for
liquid simulations) (Carlo et al. 2006).
2.2.2. Computational details
GCMC simulations were used to compute the gravimetric loadings of
hydrogen gas in the MIL-88s by using the simulation package RASPA, the
molecular simulation software for nanoporous materials (Dubbeldam et al.
2016). These simulations were performed in the VT ensembles at 77 K and
298 K, and pressures 100 bar. The number of equilibration cycles was 105
steps, followed by 3105 MC steps for the random insertion, deletion,
translation, and rotation of hydrogen molecules in the simulation box. The
framework was kept rigid during the simulation process, while the hydrogen
molecule freely moves in the MOF structure. The interaction between the H 2
gas and the atoms (C, O, H and metal) of the MOF were described through the
Lennard-Jones (LJ) 6-12 potential and the electrostatic potential:
12 6
qq
ij
ij
1 i j ,
(2.12)
U rij 4 ij
rij 4 o rij
rij
where U is the potential energy between a pair of atoms i and j at a distance rij;
εo is the dielectric constant; qi is the partial charge of atom i obtained from the
DDEC atomic net charge calculation based on the DFT method. The
parameters
and
are the LJ potential well depth and diameter. The LJ
interaction is neglected beyond the cutoff radius of 12.8 Å.
Partial charges for the atoms in MIL-88s were computed by DDEC method.
These point charges were assigned to atomic sites to compute the electrostatic
interaction. This interaction was handled using the Ewald summation technique
with the cutoff radius of 12 Å. For the hydrogen molecule, a single LJ
interaction site model at the centre of mass (Hcom) was used with the LJ
parameters were taken from the TraPPE force field (Levesque et al. 2002).
10
CHAPTER 3: HYDROGEN ADSORPTION IN Co-MIL-88A
3.1. Optimization of Co-MIL-88A unit cell
The MIL-88A was designed with the chemical formula [{M3O(-O2C-C2H2CO2-)3}]n having a 3D hexagonal structure consisting of the trimers of metal
octahedra linked to the fumarate ligands, where n is the number of chemical
formula units. Figure 3.1 shows the structure of the unit cell of Co-based MIL88A with n 2 . The cell parameters of the unit cell are a b c and the
angles 90, 120. After the primary unit cell of Co-MIL-88A
was designed, the geometry optimization for Co-MIL-88A was performed for
its volume and ionic positions that were fully relaxed by using vdW-DF (Dion
et al. 2004). By fitting based on the Murnaghan equation of state (EOS)
(Murnaghan 1951), the optimized lattice constants for the unit cell of
Co-MIL-88A are a = b = 11.222 Å and c = 14.719 Å, resulting in a volume of
1605.34 Å3.
(a)
(c)
(b)
(d)
Figure 3.1. The unit cell of Co-MIL-88A: (a) side view, (b) top view of the unit cell, (c) μ3-Ocentered trimer of Co metals, and (d) fumarate ligand of MIL-88A.
3.2. Searching stable hydrogen adsorption sites
When obtaining the optimized Co-MIL-88A unit cell, a hydrogen molecule
(H2) is loaded into the structure at many different sites, and then geometry
optimization is performed and the adsorption energy of H2 in Co-MIL-88A is
calculated. The results are listed in Table 3.1 together with the average bond
length of H2 to the closest atoms of the MOF.
Table 3.1. The adsorption energy (Eads) for the favourable adsorption sites. The average distance
between H2 and the reference atoms of the MOF (
) and the Bader point charge of H2 ( ).
Sites
Hollow
Ligand
Metal (side-on)
Metal (end-on)
Eads (kJ/mol)
-13.72
-10.76
-10.61
-6.50
Eb (kJ/mol)
13.72
10.76
10.61
6.50
11
(Å)
3.20
3.41
3.14
3.15
(e)
-0.0002
-0.0006
-0.0038
-0.0006
The results show the favourable adsorption site is in the order of hollow >
ligand > metal side-on > metal end-on. The most favourable adsorption of H2 is
at the hollow site between two COO- groups linked to Co atoms. At this
position, the H2-MIL-88A binding energy is 13.72 kJ/mol. The reason for the
stronger adsorption of H2 on the organic ligand compared to the metal site may
be due to the relatively short fumarate bridges. Thereby, the metal and oxygen
atoms may interact with the H2 located at the hollow and ligand sites. For the
H2 adsorbed end-on configuration on the metal site, the binding energy of this
configuration is the smallest compared with that of the others.
For deeper insights into the H2@MIL-88A interaction, the electronic
properties are analyzed through CDD and DOS. The CDD between H2 and CoMIL-88A is shown in Figure 3.2. For the hollow, ligand, and side-on (metal)
configurations, the H2 molecule interacts with the Co-MIL-88A through its
bonding () state, while the anti-bonding (*) state of H2 interacts with CoMIL-88A at the end-on site. The charge exchange cloud of the H2 molecule
closest to the MOF shows a charge gain for the cases of the H2 molecule
adsorbed on the ligand, side-on, and end-on sites via the yellow clouds;
however, it shows a charge donation for the hollow site with the most
favourable adsorption (cyan cloud). The hollow configuration (Figure 3.2a) has
the largest charge exchange cloud due to the strongest interaction of H2 with
the MOF, while the end-on configuration on the metal (Figure 3.2b) has the
smallest charge exchange cloud because of the weakest interaction.
a) Hollow
b) Ligand
c) Metal (side-on)
d) Metal (end-on)
Figure 3.2. CDD for the favourable adsorption configurations of H2 in Co-MIL-88A. The
orbitals are drawn at an isosurface value of 0.0002 e/Bohr3. Yellow (positive) and cyan
(negative) clouds indicate charge gain and loss.
The Bader charge exchange of H2 in Co-MIL-88A is also listed in Table 3.1.
The result shows that the Bader charge of the adsorbed H2 is very small and
within the error of the charge calculation of 0.0005 e. Therefore, it can be
concluded that there is no significant charge transfer between H2 and Co-MIL88A because of the weak physisorption of the H2 molecule in the MOF.
A deeper understanding of the MOF – H2 interaction can be exposed
through the overlapping of DOS curves describing the interaction between H2
and Co atoms of the MIL-88A. Figure 3.3 indicates the bonding state () of H2
12
DOS (States per eV)
overlaps with the d orbitals of the Co atoms. For the hollow, the ligand, and the
metal side-on configurations, the
,
and
orbitals of the metal
atoms mainly contribute to the interaction with H2, while it is the
orbital for
the metal end-on configuration. The s orbital of the Co atoms of the MOF also
contributes to the interaction with H2 but most substantially for the most
favourable H2 adsorption configuration, on the hollow site. Although the H2
molecule at the hollow site is far away from the nearest Co atoms with the
average distance of 4.15 Å, the interaction of the H2 with the Co atoms is still
possible through the indirect interaction with the oxygen atoms in the outer
space of the metal oxide. Figure 3.4 elucidates the interaction between H2 and
Co atoms via the real-space wave functions (Feenstra et al. 2013), showing that
there is an overlapping between the wave function of the H atoms of the H 2
molecule and that of the Co atoms.
E-EF (eV)
Figure 3.3. DOS of the hydrogen molecule and the s and d orbitals of the Co atoms of the CoMIL-88A at the sites: hollow (a), ligand (b), metal side-on (c), and metal end-on (d).
Figure 3.4. The real part of the wave functions of the H atom of H2 and the Co atom of MIL-88A
along the x-direction. The dots denote for the position of the atoms.
13
Remarkably, the H2@Co-MIL-88A interaction strength is quantitatively
assessed by calculating an overlapping of DOS (Hoffmann 1988), which is the
overlap area between the DOS of the adsorbed H2 and the DOS of the atomic
orbitals of Co-MIL-88A. The calculated results are listed in column 7 of Table
3.2. It indicates that overlapping DOS correlates with the binding energy, i.e.,
the larger the overlapping of DOS is, the stronger the binding strength
becomes. The last column of Table 3.2 also shows that the more stable the H2
adsorption configuration becomes, the lower the peak height of the H2 DOS is,
i.e. the DOS area of the H2 molecule adsorbed in Co-MIL-88A decreases
versus the increase in the H2@Co-MIL-88A interaction. Table 3.2 shows that
the overlapping of the H2 DOS with the s, d orbitals of Co atoms and the p
orbital of the 3-O atoms monotonically increase in the order: the metal end-on,
the metal side-on, the ligand, the hollow site. In general, the inner atoms of the
trimers such as Co and 3-O become more and more important for stabilizing
the H2 adsorption.
Table 3.2. Overlapping DOS between the DOS of the adsorbed hydrogen molecule with the
DOS of different components of Co-MIL-88A.
Sites
Hollow
Ligand
Metal side-on
Metal end-on
d
orbital
of Co
s
orbital
of Co
s and d
orbitals
of Co
0.750
0.704
0.376
0.258
0.378
0.180
0.081
0.017
1.128
0.884
0.457
0.275
p
orbital
of 3-O
atoms
0.793
0.731
0.250
0.049
Total p
orbital
of all
atoms
1.277
1.400
1.433
1.488
Total
DOS of
all atoms
Area
of H2
DOS
2.405
2.284
1.890
1.763
0.7050
0.7052
0.7358
0.7836
3.3. Adsorption isotherms of hydrogen in Co-MIL-88A
In order to determine hydrogen uptakes in Co-MIL-88A, the point charges
of the atoms (Co, C, O, and H) are computed by the DDEC method based on
DFT calculations combining to the LJ parameters are taken in generic force
fields (UFF) for MOFs. For assessment of the adsorption capacity of H2 in CoMIL-88A at temperatures of 77 K and 298 K and pressures up to 100 bar, the
average amount of absolute and excess uptakes was computed. Typically, for
physisorption system, the scope of the isotherms in Figure 3.5 represents type-I
adsorption isotherm in the IUPAC classification (Sing et al. 1982). Figure 3.5a
shows that the H2 adsorption isotherms at 77 K increase sharply below 5 bar
and achieves the maximum value of about 4.0 wt% at 12 bar for the excess
uptake but still increases slightly for the absolute uptake until 100 bar and
reaches the value of 4.6 wt%. From these results, we see the H2 uptake in CoMIL-88A at the cryogenic temperature (77 K) is moderate compared with that
of the best MOFs reported up to now, see the above section for the overview of
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